Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Vol 128 (4) ◽  
pp. 671-679 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations failed to capture completely the total expansion effect on the flow, which is influenced by both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When two-dimensional simulations were performed using the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations were compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, thus sustaining laminar flow symmetry to higher Reynolds numbers. Last, and most important, when the logarithm of the critical Reynolds number was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Analysis of the Fluid Flow in 3D Symmetric Enlarged Channel

2015 ◽  
Vol 813-814 ◽  
pp. 652-657
Author(s):  
Seranthian Ramanathan ◽  
M.R. Thansekhar ◽  
P. Rajesh Kanna ◽  
S. Shankara Narayanan
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Software Package ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
3 Dimensional ◽  
Ansys Workbench

A 3-Dimensional fluid flow over the sudden expansion region of a horizontal duct for various Reynolds numbers have been studied by using the CFD Software package ANSYS Workbench Fluent v 13.0. The expansion ratio and aspect ratio for the sudden expansion are taken as 2.5 and 4 respectively. This work deals with the finding of critical Reynolds number for a fluid and also the length of re-attachments on stepped walls at various Reynolds numbers for the same fluid. The simulation is carried out in sudden expansion for Reynolds number ranging from 200 to 4000. The variations of local Nusselt number along the stepped walls of the sudden expansion are presented with the heat flux of 35 W/m2 on the stepped walls. Also, the plots of pressure coefficient (Cp) along the stepped walls for different Reynolds numbers are presented in this work.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

Global stability of multiple solutions in plane sudden-expansion flow

2012 ◽  
Vol 702 ◽  
pp. 378-402 ◽  
Author(s):  
Daniel Lanzerstorfer ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Secondary Flow ◽  
Mirror Symmetry ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Secondary Flows ◽  
Sudden Expansion ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Large Expansion

AbstractThe two-dimensional, incompressible flow in a plane sudden expansion is investigated numerically for a systematic variation of the geometry, covering expansion ratios (steps-to-outlet heights) from $0. 25$ to $0. 95$. By means of a three-dimensional linear stability analysis global temporal modes are scrutinized. In a symmetric expansion the primary bifurcation is stationary and two-dimensional, breaking the mirror symmetry with respect to the mid-plane. The secondary asymmetric flow experiences a secondary instability to different three-dimensional modes, depending on the expansion ratio. For a moderately asymmetric expansion only one of the two secondary flows (the connected branch) is realized at low Reynolds numbers. Since the perturbed secondary flow does not deviate much from the symmetric secondary flow, both secondary stability boundaries are very close to each other. For very small and very large expansion ratios an asymptotic behaviour is found for suitably scaled critical Reynolds numbers and wavenumbers. Representative instabilities are analysed in detail using an a posteriori energy transfer analysis to reveal the physical nature of the instabilities. Depending on the geometry, pure centrifugal and elliptical amplification processes are identified. We also find that the basic flow can become unstable due to the effects of flow deceleration, streamline convergence and high shear stresses, respectively.

Analysis of Fluid Flow in Porous Media Using the Lattice Boltzmann Method: Inertial Flow Regime

2012 ◽  
Author(s):  
Huizhe Zhao ◽  
Aydin Nabovati ◽  
Cristina H. Amon
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Inertial Flow ◽  
Boltzmann Method ◽  
Three Dimensional Simulations

In this work, we use the lattice Boltzmann method to study inertial flow in three-dimensional random fibrous porous materials. In order to validate the methodology, inertial flow in two-dimensional hexagonal arrangements of circular cylinders is simulated, and the results are compared against those previously reported in the literature. The three-dimensional fibrous porous materials are then constructed by randomly placing straight cylindrical fibers inside the computational domain. Inertial effects are studied systematically for a wide range of pore Reynolds numbers in materials with porosities between 0.60 and 0.95. A previously proposed semi-empirical relation is modified to represent the inertial effects in three-dimensional fibrous materials. Three distinct regimes of constant, quadratic, and linear relations between the inverse of the permeability and pore Reynolds number are observed for both two- and three-dimensional simulations. The critical Reynolds number, beyond which the inertial effects are strong and this relation is linear, is shown to be smaller in three-dimensional simulations, when compared to the critical Reynolds number in two-dimensional simulations.

scholarly journals Three-dimensional Floquet stability analysis of the wake of a circular cylinder

1996 ◽  
Vol 322 ◽  
pp. 215-241 ◽  
Author(s):  
Dwight Barkley ◽  
Ronald D. Henderson
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Mode A

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.

scholarly journals Three-dimensional instability in flow over a backward-facing step

2002 ◽  
Vol 473 ◽  
pp. 167-190 ◽  
Author(s):  
DWIGHT BARKLEY ◽  
M. GABRIELA M. GOMES ◽  
RONALD D. HENDERSON
Keyword(s):  
Reynolds Number ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Linear Instability ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Computational Stability ◽  
Two Dimensional Flow

Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.

Bifurcation analysis of two-dimensional laminar flow through sudden expansion channel

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Laminar Flow ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Bifurcation Phenomena ◽  
Different Types ◽  
Fluent Software ◽  
Flow Through ◽  
Volume Method

In this work, bifurcation characteristics of unsteady, viscous, Newtonian laminar flow in two-dimensional sudden expansion and sudden contraction-expansion channels have been studied for different values of expansion ratio. The governing equations have been solved using finite volume method and FLUENT software has been employed to visualize the simulation results. Three different mesh studies have been performed to calculate critical Reynolds number (Recr) for different types of bifurcation phenomena. It is found that Recr decreases with the increase in expansion ratio (ER).

Two- and Three-Dimensional Simulations of the Flow Around a Cylinder Fitted With Strakes

2012 ◽  
Author(s):  
Bruno S. Carmo ◽  
Rafael S. Gioria ◽  
Ivan Korkischko ◽  
Cesar M. Freire ◽  
Julio R. Meneghini
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
The Body ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Flow Around A Cylinder ◽  
Three Dimensional Simulations ◽  
Angle Of Rotation

Two- and three-dimensional simulations of the flow around straked cylinders are presented. For the two-dimensional simulations we used the Spectral/hp Element Method, and carried out simulations for five different angles of rotation of the cylinder with respect to the free stream. Fixed and elastically-mounted cylinders were tested, and the Reynolds number was kept constant and equal to 150. The results were compared to those obtained from the simulation of the flow around a bare cylinder under the same conditions. We observed that the two-dimensional strakes are not effective in suppressing the vibration of the cylinders, but also noticed that the responses were completely different even with a slight change in the angle of rotation of the body. The three-dimensional results showed that there are two mechanisms of suppression: the main one is the decrease in the vortex shedding correlation along the span, whilst a secondary one is the vortex wake formation farther downstream.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

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